Alpine made the announcement at the Spanish Grand Prix. The Italian businessman will have an "executive advisor" role, the team said.
Briatore, 74, was the team principal at Benetton and Renault, the previous iterations of Alpine, in the 1990s and 2000s. Under his leadership, Michael Schumacher won championships in 1994 and 1995 for Benetton while Fernando Alonso won the 2004 and 2005 titles under Renault.
Briatore left F1 after being found guilty of ordering Nelson Piquet Jr. to deliberately crash his car to help teammate Alonso win the Singapore Grand Prix in 2008.
He was initially handed a life ban by governing body FIA but he took the matter to a French court and successfully overturned the punishment.
Alpine has struggled this season, scoring just five points from nine races. The team said in May that it would part ways in 2025 with Esteban Ocon, the only driver to win a race for the team since it rebranded from Renault in 2020.
Briatore was also part-owner and chairman of English soccer club Queens Park Rangers from 2007-10.